Loops, multi-edges and collisions in supersingular isogeny graphs (Q6584302)

This paper provides a detailed examination of the structural properties of supersingular isogeny graphs, focusing on loops, multi-edges, and collisions. The author establishes bounds on these features and presents conditions under which the graphs are simple, making the work particularly relevant to post-quantum cryptography. The research is grounded in solid mathematical theory, utilizing Brandt matrices and Hurwitz class numbers to support the findings.\N\NThe introduction of the bi-route number adds a novel aspect to the study, offering insights into the similarities between different isogeny graphs. Overall, the paper makes a valuable contribution to the understanding of these graphs, with significant implications for cryptographic applications.